Homework SourseThe managers of a brokerage firm are interested in finding o
The managers of a brokerage firm are interested in finding out if the number of new clients (independent variable) a broker brings into the firm affects the sales (dependent variable) generated by the broker (independent variable). They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
Broker Clients Sales
1 27 52
2 11 37
3 42 64
4 33 55
5 15 29
6 15 34
7 25 58
8 36 59
9 28 44
10 30 48
11 17 31
a. Is the estimate of the slope for the Y-intercept significant at the 95% confidence level? Explain.
b. What does the estimate of the Y-intercept mean in relation to the problem facing the brokerage firm?
c. How much in sales (in $1,000s) does the regression predict for a broker who brings 25 new clients into the firm?
d. What percentage of the total variation in sales generated can be explained by the number of new clients brought in?
e. What does the model predict for the case where the broker brings in 35 new clients?
Solution
Thus, the regression equation :
sales = 18.46 + 1.103 (Clients)
The intercept gives the amount of sales if there are no brought in by the brokers.
The value of intercept is significant at 95% confidence interval, as p-value < 0.005
Sales = 18.46 + 1.103 (25)
= 46.05 is the sales when 25 new clients are brought in
Similarly,
sales = 18.46 + 1.103 (35)
= 57.09 is the sales when 35 new clients are brought in
The percentage of variation explained is given by the R-squared value:
= 78.8 %
Hope this helps. Thanks
Ask if you have any doubts
| Broker | Client | Sales |
| 1 | 27 | 52 |
| 2 | 11 | 37 |
| 3 | 42 | 64 |
| 4 | 33 | 55 |
| 5 | 15 | 29 |
| 6 | 15 | 34 |
| 7 | 25 | 58 |
| 8 | 36 | 59 |
| 9 | 28 | 44 |
| 10 | 30 | 48 |
| 11 | 17 | 31 |
